Belgium, Luxembourg or Netherlands

Belgium has dozens of exclaves in the Netherlands (Baarle Hertog, Baarle Nassau), just south of Tilburg. Look at it on Google maps, it's quite amusing. There are actually Dutch exclaves within the Belgian exclaves, within the Netherlands.

The ABC islands are not exclaves. An island by definition is surrounded by water, whereas an exclave, by definition, is surrounded by foreign territory.

If that's what you mean, then I would suggest changing the wording of the question to reflect that. The way it's written now is very confusing. It would in fact be hard to nail down whether dutch originated in the Netherlands or in Flanders first, whether it co-evolved in both locations, given that Belgium and the Netherlands were part of the same country/kingdom for much of the language's evolutionary past.

I would probably just put in an entirely different question. It is too complex an issue. In your own reply you just said that "Flanders has its own language, Vlaams". This then automatically negates the answer to your question about which country does not have its own language. I don't think you can nail down "ownership" of the "Nederlands" language, and that doesn't even begin to cover the regionally official language status of Friesian (is it unique to Netherlands, or is it similar enough to East Frisian in Germany???). Lots of other good questions available about BENELUX!